lecture 8 - correlation

Question 1

what data types are on each axis?

Answer 1

ratio or interval

Question 2

what variables are on each axis?

Answer 2

y - dependent
x - independent

Question 3

what happens if one factors increases?

Answer 3

if one increases the other does too:
COVARIANCE
Co-vary
or vary together

Question 4

what is correlation?

Answer 4

correlation
+ or - and strength
scale independent of the variables, between -1 and 1
standardised - think z-score

Question 5

what is covariance?

Answer 5

+ or -
scaled to the variable
no upper or lower limit
not standarised

Question 6

when are two variables said to be co-related?

Answer 6

“when the variation of the one is accompanied on the average buy more or less vacation of the other, and in the same direction”

Question 7

what does Pearson’s correlation coefficient describe?

Answer 7

correlation coefficient (r) quantifies the strength and direction of a linear association between two variables

Question 8

how are strengths classified for negative correlation?

Answer 8

(-1) - perfect
(-0.7) - (-0.9) - strong
(-0.4) - (-0.6) - moderate
(-0.1) - (-0.3) - weak
0 - zero

Question 9

how are strengths classified for positive correlation?

Answer 9

(1) - perfect
(0.7) - (0.9) - strong
(0.4) - (0.6) - moderate
(0.1) - (0.3) - weak
0 - zero

Question 10

are correlation and causation the same?

Answer 10

• correlation does not = causation
• third or confounding variable problem
• direction of causality

Question 11

how are correlations often displayed?

Answer 11

correlation matrix

Question 12

what are the assumptions?

Answer 12

• ratio/interval
• normally distributed
• independent
• linear
• homoscedasticity (variation of data along line of best fit should not change (variation on each side should be the same))
• different from t-test

Question 13

what is the null hypothesis for correlation?

Answer 13

H0 - there is no association between … and ….
any association found is simply a result of sampling error

Question 14

what is the alternation hypothesis for correlation?

Answer 14

H1 - there is an association between the … and ….

Question 15

which bits do you look at in the table?

Answer 15

Pearson’s correlation coefficient - direction and strength

sig. (2-tailed) - significance

N - sample size

Question 16

what is the coefficient of determination?

Answer 16

correlation - they co-very, share a variance
of r = 0.106 and r^2 = 0.011
coefficient of determination - 1.1%
residual variance - 98.9%

Question 17

what does the coefficient of determination mean?

Answer 17

1.1% of variability in total triathlon time can be explained by the time in the swimming leg

Question 18

how do we report correlation

Answer 18

r(degrees of freedom (N-2)) = the r statistic, p=p value

Question 19

when do we reject H0 in one and two-tailed tests?

Answer 19

• with a two-tailed test we would reject H0 if we found a positive or negative association
• with a one-tailed test, we only reject H0 if the association is in the direction that we expected and half the p value in the output

Question 20

what is Spearman’s rho (Rs) rank correlation?

Answer 20

• non parametric equivalent of Pearson’s r
• one or both variables are ordinal
• ratio/interval but the parametric assumptions have been violated/breached
• spearman’s rho calculates the ranked scores for each variable and considers the association between the ranks
• minimum sample size of 20

Question 21

what is Kendall’s Tau test?

Answer 21

nonparametric and one or both variables are ordinal or ratio
- useful with N<20
- can deal with large number of tied ranks in the data